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[Emergence of Superconductivity at 20 K in Th3P4-type In3-x S4 Synthesized by Diamond Anvil Cell with Boron-Doped Diamond Electrodes.pdf](https://mdr.nims.go.jp/filesets/353e89db-e3bd-4d10-8601-1341a36c389c/download)

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[Ryo Matsumoto](https://orcid.org/0000-0001-6294-5403), [Kazuki Yamane](https://orcid.org/0000-0002-0162-5411), [Terumasa Tadano](https://orcid.org/0000-0002-8132-2161), [Kensei Terashima](https://orcid.org/0000-0003-0375-3043), Toru Shinmei, Tetsuo Irifune, [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928)

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his document is the Accepted Manuscript version of a Published Work that appeared in final form in Chemistry of Materials, copyright © 2025 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.chemmater.4c03301.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Emergence of Superconductivity at 20 K in Th<sub>3</sub>P<sub>4</sub>-type In<sub>3–<i>x</i></sub>S<sub>4</sub> Synthesized by Diamond Anvil Cell with Boron-Doped Diamond Electrodes](https://mdr.nims.go.jp/datasets/4359b8b8-fc0a-4204-acb8-33756b27cfc9)

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1 Emergence of Superconductivity at 20 K in Th3P4-type  In3−xS4 Synthesized by Diamond Anvil Cell with Boron-doped Diamond Electrodes   *R. Matsumoto1, K. Yamane1,2, T. Tadano3, K. Terashima1, T. Shinmei4, T. Irifune4, Y. Takano1,2 *Corresponding author; Email: MATSUMOTO.Ryo@nims.go.jp  1International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 2Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan 3Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 4Geodynamics Research Center (GRC), Ehime University, Matsuyama, Ehime 790-8577, Japan  Keywords: Superconductivity, high pressure, Indium sulfide, diamond anvil cell  Abstract The exploration of superconductors in metastable phases by manipulating crystal structures through high-pressure techniques has attracted significant interest in materials science to achieve a high critical temperature (Tc). In this study, we report an emergence of novel superconductivity in a metastable phase of Th3P4-type cubic In3−xS4 with remarkably high Tc at 20 K under 45 GPa by using an originally designed diamond anvil cell equipped with boron-doped diamond electrodes, which can perform a high-pressure synthesis and an in-situ electrical transport measurement simultaneously. In-situ structural analysis indicates that the In3−xS4 appears partially above 40 GPa without heating. The high-pressure annealing treatment induces complete transformation to the Th3P4-type structure, and the defected concentration of x in In3−xS4 decreases with increasing annealing temperature. The Tc in In3−xS4 is maximized at x = 0 and approaches 20 K. Electronic band calculations show that the high density of states composed of sulfur and indium bands are located at the conduction band bottom near Fermi energy. The record high Tc in In3−xS4 among superconducting sulfides accelerates the further exploration of high Tc materials within the Th3P4-type cubic family by using flexibility in crystal structure.  2 1. Introduction Since the discovery of superconductivity in mercury[1], the exploration of superconducting materials with higher transition temperature (Tc) has been continued, driven by their potential for ultimate energy-saving applications based on unique properties, such as zero resistivity. The Tc has grown typically through a search for stable phases by varying the composed elements and synthesis temperature, as seen in the discovery of high-Tc cuprates[2,3] and Fe-based materials[4]. However, such exploration has gradually tended to saturate due to the limited space of materials design. High-pressure application is a promising tool for expanding this space by stabilizing metastable phases by manipulating crystal structures. Most record Tc values are achieved under high pressure in various superconducting families, such as HgBa2Ca2Cu3O8+δ (Tc = 164 K at 20 GPa) in cuprates[5,6], La(O,F)BiS2 (Tc = 10 K at 1 GPa) in BiS2-based materials[7,8], TaS2 (Tc = 16.4 K at 157.4 GPa) in transition-metal dichalcogenides[9], and LaH10 (Tc = 260 K at 188 GPa) in hydrides[10,11]. Recently discovered high-Tcs in nickelates of La3Ni2O7[12] and La4Ni3O10[13] also represent metastable phases under high pressure. Investigating novel metastable phases in different material groups has attracted considerable interest in discovering high-Tc superconductors.  A group of compounds crystallizing in the Th3P4-type cubic structure offers significant freedom in designing functionality, as the Th and P sites can be replaced by various (cation)4+ and (anion)3− species, such as Sr, Ti, Zr, Hf, Th, U, Np in the Th site, and N, P, As in the P site. Additionally, (cation)3+ and (anion)2− can be accepted by introducing defects in the Th site, such as Y, lanthanoids (Ln), excluding Pm, Ac, Pu, Am, Cm, Bk, Cf in the Th site, and chalcogens (Ch) of S, Se, Te in the P site. By utilizing the compositional flexibility, various functional materials in this structure have been designed, including thermoelectric materials[14,15], ultrahard materials[16,17], and others[18]. The research for superconductivity in this structure has been conducted before the discovery of cuprate, and relatively high Tc was reported. In particular, La3−xCh4 shows superconductivity at ambient pressure with a Tc of 8.3 K in La3−xS4[19] and 8.5 K in La3−xSe4[20]. Recent first-principles calculations predict the emergence of superconductivity in several metastable Th3P4-type materials under high pressure[21–23]. Among these predictions, Sn3S4 is estimated to have the highest Tc [22], and the superconductivity with Tc of 12 K at 5.6 GPa is confirmed experimentally through high-pressure synthesis.[24]. However, the exploration of superconductors in the metastable phase of this family with varying compositions is still an open issue due to the difficulty in the sample synthesis and in-situ measurements of physical properties under high pressure.   In this study, we focus on the Th3P4-type cubic In3−xS4 as a candidate for a superconductor. The stable phase at ambient pressure for the In3−xS4 is the layered tetragonal structure of In2S3[25]. The cubic In3−xS4 is obtained as a metastable phase via high-pressure annealing of the tetragonal In2S3[26]. The defect concentration of x in In3−xS4 is typically 0.33 when the In2S3 is homogeneously transformed to the Th3P4-type structure. Even though a similar compound of Th3P4-type In3−xSe4 is obtained from  3 In2Se3 by the compression and exhibit superconductivity[27], knowledge of the physical properties, particularly the emergence of superconductivity, is still lacking for In3−xS4. Understanding the physical properties of In3−xS4 provides valuable insights for future exploration of superconductors in this family. We have conducted high-pressure annealing and in-situ characterization for tetragonal In2S3 under various conditions and obtained Th3P4-type In3−xS4 using a diamond anvil cell (DAC) high-pressure apparatus. The crystal structure, including the defected amount of In, was quantitively investigated using synchrotron X-ray diffraction (SXRD) analysis in the DAC during compression. In-situ electrical transport measurements of the obtained In3−xS4 were performed in the same chamber of DAC used for SXRD analysis. Our high-pressure research successfully reveals that Th3P4-type In3−xS4 exhibits a surprisingly high Tc of 20 K. The superconducting properties are strongly related to the deficiency in the In site. The first-principles calculations indicated that the electronic states of the non-defected In3S4 are mainly composed of In and S bands with comparable contribution, which totally differs from typically known high-Tc sulfides. The discovery of superconductivity in In3−xS4 opens avenues for further exploration of advanced materials, as its Tc is the highest record among binary sulfides, except for high-Tc hydrides[28,29].  2. Results and discussion 2.1 Synthesis of Th3P4-type In3−xS4 Th3P4-type In3−xS4 was synthesized via high-pressure annealing for tetragonal In2S3 using a specially designed DAC, as shown in Fig. 1 (a). Boron-doped diamond (BDD) with a high boron concentration above 1021 cm−3, which exhibits metallic transport property[30], is fabricated onto the surface of the diamond anvil as electrodes for electrical measurements[31–33]. The BDD heater and thermometer are positioned near the sample space for temperature control during high-pressure annealing[24,34]. A small piece of tetragonal In2S3 is placed in the center of the diamond anvil, as depicted in Fig. 1 (b). The sample was compressed by squeezing the DAC to above 30 GPa and then annealed using the BDD heater while measuring electrical resistance in the DAC. Figure 1 (c) shows a typical behavior of resistance and temperature sequence during high-pressure annealing to obtain Th3P4-type In3−xS4. The compressed In2S3 initially exhibits semiconducting behavior with decreasing resistance as temperature increases. At around 350 K, the resistance continues to reduce even with constant temperature, indicating progress of structural phase transition from tetragonal In2S3 to a lower resistance phase. Consequently, metallic properties with increasing resistance against temperature are observed above 400 K and the cooling process.   4  FIG. 1. (a) Schematic image of diamond anvil cell (DAC) with boron-doped diamond (BDD) components. (b) Optical microscope image of the mounted tetragonal In2S3 onto the diamond anvil. (c) Typical behavior of the resistance during the high-pressure annealing to obtain Th3P4-type In3−xS4. The upper figure is the temperature sequence, and the lower one is the change in the electrical resistance of the sample.  Figure 2 presents a typical SXRD pattern along with the result from Rietveld refinement for the sample at 45 GPa after high-pressure annealing. The green and gray bars indicate simulated peak positions for Th3P4-type In3S4 and cubic BN as a pressure-transmitting medium, respectively. The blue spectrum represents the differential curve in the fitting. The analysis reveals that the sample crystallizes with a Th3P4-type cubic structure (I-43d) with no detectable impurity phases. The derived lattice parameter is a = 7.5309 Å with a reliability factor Rwp = 0.817%, which qualitatively agrees with a previous report of the high-pressure synthesis of Th3P4-type In3−xS4 via laser heating in a DAC[26]. Although these SXRD results are obtained from the sample sintered under 44 GPa and 1100 K, the Th3P4-type structure has appeared at lower pressure and temperature conditions below 41 GPa and 600 K, as shown in Fig. S1. These results suggest that the phase transition from tetragonal In2S3 to Th3P4-type In3−xS4 occurs near the boundary of semiconductor to metal transition, as discussed in Fig. 1 (c). Additionally, the sample partially exhibits a signature of a Th3P4-type diffraction pattern even before annealing, indicating that the In3−xS4 phase begins to form at room temperature. A similar trend of pressure-induced transformation to the Th3P4-type phase without heating has been observed for In3−xSe4[27]. The Th3P4-type structure rapidly decomposes with decreasing pressure, as shown in the SXRD patterns during the decompression process in Fig. S2. The behavior of instability in In3−xS4, 0 5 10 15 20 25 3015202530354045Time (min)Resistance (Ω)Diamond anvilGasketCompressionBDD electrodesElectrical measurementsBDD heater & thermometerTemperature controlTetragonal In2S3SemiconductingPhase transition(In2S3 to In3-xS4)MetallicHeating CoolingMetallic300400500600Temperature (K)41 GPaHeating Cooling(a)(c)(b) 5 indicating a low energy barrier between the low-pressure phase and Th3P4-type structure, contrasts significantly with related compounds such as Sn3S4, which requires annealing at above 30 GPa to achieve the Th3P4-type structure and remains stable down to 5 GPa[24].   FIG. 2. SXRD patterns with synchrotron radiation (λ = 0.4171 Å) of obtained In3−xS4 under 45 GPa with the fitting result of Rietveld refinement. The green and gray bars indicate the peak positions of In3S4 and cubic BN as a pressure-transmitting medium. The blue spectrum means a differential curve for the fitting. The schematic image of the crystal structure of In3−xS4 is shown in the inset.  2.2 Superconducting properties  Figure 3 (a) shows the temperature (T) dependence of resistance (R) up to 300 K in Th3P4-type In3−xS4 at 45 GPa. The same sample of the SXRD analysis, as indicated in Fig. 2, is used for the electrical measurement. An expanded plot of the low-temperature region is displayed in the inset of Fig. 3 (a). The Th3P4-type In3−xS4 exhibits metallic transport properties with a clear drop in resistance to zero, corresponding to superconductivity emerging around 20 K. As shown in the inset, the resistance curve in the low-temperature region is well-fitted with the Bloch-Gruneisen (BG) equation, described by the following equation[35], 𝑅(T)=𝑅0+A (TθD)5∫x5(ex-1)(1-e-x)dxθD T⁄0 where R0 is the residual resistance, A is a characteristic constant, and θD is the Debye temperature. The parameters are R0 = 0.0333 Ω, A = 0.141, and θD = 171 K. The estimated θD, which serves as a proportionality constant for Tc within Bardeen-Cooper-Schrieffer (BCS) theory[36,37], is significantly lower than that of other superconducting families with comparable Tc, such as A15-type compounds[38]. One possible reason for the high Tc in In3−xS4 is the high electronic density of state (DOS) at Fermi energy (EF), which generally enhances the Tc[39]. Additionally, the sample before high-pressure annealing also exhibits a superconducting transition at 9 K, although the R-T curve is non-metallic and zero resistance is not observed, as shown in Fig. S3. According to previous SXRD analyses, tetragonal 6 8 10 12 14 16 18Intensity (a. u.)2θ (deg.)In3S4cBNSIn45 GPa 6 In2S3, which is stable at ambient conditions, undergoes several structural phase transitions under high pressure from phase I to phase III to an amorphous state[25,26,40]. In our SXRD analysis, amorphous-like broadened diffraction peaks are consistently observed before annealing at 41 GPa. On the other hand, small peaks corresponding to the Th3P4-type structure are also visible in the diffraction patterns before annealing. These observations indicate that the signature of superconductivity with Tc = 9 K in as-pressed sample also originates from Th3P4-type In3−xS4, and the Tc significantly enhances to 20 K via annealing. The modulation of Tc is possibly related to changes in the amount of In defects because similar modifications in defect amounts occur in other Th3P4-type compounds, affecting their physical properties, such as in superconducting Y3−xS4[41,42] and high-temperature thermoelectric material La3−xTe4[43].  Figure 3 (b) depicts the enlarged R-T curve of Th3P4-type In3−xS4 in the low-temperature region under various magnetic fields to detail the superconducting transition. The inset shows a more enlarged plot around the starting temperature of the drop in resistance, defined as Tconset. Comparison of the R-T curves under 0 and 7 T reveals that the Tconset of In3−xS4 at 45 GPa is 20.0 K, while the temperature at zero resistance (Tczero) is 17.2 K. The superconducting transition is gradually suppressed by applying magnetic fields up to 7 T. The upper critical field μ0Hc2(0) is estimated using the temperature dependence of μ0Hc2, as shown in Fig. 3 (c). The criterion used to determine Tc under each magnetic field is the temperature at 99% of normal resistance. The plot with Werthamer-Helfand-Hohenberg (WHH) fitting[44,45] reveals a μ0Hc2(0) of 31.7 T, which is comparable to the weak-coupling Pauli limit (1.84Tc = 36.4 T). This behavior contrasts with isostructural La3−xS4, which exhibits higher μ0Hc2(0) than 1.84Tc[46]. The coherence length at zero temperature ξ(0) is determined to be 3.2 nm from the Ginzburg-Landau (GL) formula μ0Hc2(0) = Φ0/2πξ(0)2, where the Φ0 is a fluxoid.   FIG. 3. Results of electrical transport measurements under high-pressure in obtained In3−xS4. (a) Temperature (T) dependence of resistance (R) at 45 GPa. The inset shows the enlarged plot below 100 K with BG fitting. (b) R-T curves under magnetic fields. The onset Tc is defined by the separating point of the R-T curve under 0 and 7 T, as presented in the inset. (c) Temperature dependence of μ0Hc2.  00.010.020.030.0412 14 16 18 20 22 24 26Temperature (K)00.020.040.060.080.10 50 100 150 200 250 300Temperature (K)Resistance (Ω)0.0310.0320.0330.0340.03517 18 19 20 21 2220 K →051015202530350 5 10 15 20 25Temperature (K)μ0Hc2 (T)μ0Hc2(0) = 31.7 Tξ(0) = 3.2 nm(a) (b) (c)0.030.040.0520 40 60 80 1000 T1 T2345677 T0 T45 GPa 45 GPa45 GPa 7 Figure 4 (a) shows the variation of Tc in In3−xS4 under different annealing conditions from our experimental runs. The remarkably high Tc in In3−xS4 is reproducibly observed. Moreover, a positive trend between Tc and annealing temperature is indicated across a range of 14 to 20 K, although pressure values in each plot are slightly different. To investigate the reasons for Tc variation, we performed an SXRD analysis for each sample after annealing in Run5 and estimated the amount of In deficiency based on occupancy analysis using Rietveld refinements. Figure 4 (b) presents the relationship between the amount of In defect and Tc in In3−xS4, with labeled values representing the annealing temperature. The amount of In defects x decreases monotonically with the increase of annealing temperature and approaches zero in the sample sintered at 1100 K, which has the highest Tc of 20 K. Additionally, the Tc in as-pressed sample is plotted as In2.67S4, and the plot smoothly connects to the annealed samples. These observations suggest that the starting material In2S3 transforms into superconducting Th3P4-type In3−xS4 with Tc of 9 K through compression without the annealing treatment. The Tc of Th3P4-type In3−xS4 can be widely tuned up to 20 K by modifying the amount of In deficiency via high-pressure annealing. A potential concern is the generation of pure sulfur as an impurity in the sample chamber, known as a superconductor with Tc of 15 K[47] because the initial In2.67S4 transforms to In3S4 during sintering. We believe that the observed high Tc of 20 K originates from In3S4, as the metallic phase of sulfur-III with an orthorhombic structure should appear above 80 GPa, which is significantly higher than our experimental conditions[48–50].   FIG. 4. (a) The obtained Tc in In3−xS4 sintered by various temperatures. The annealing pressures (GPa) are labeled near each plot. (b) In amount dependence of Tc in In3−xS4. The dashed line is a guide for the eye.     500 600 700 800 900 1000 1100 1200121416182022Annealing temperature (K)Tconset  (K)0 0.05 0.1 0.15 0.2 0.25 0.3 0.356810121416182022x in In3-xS4Tconset  (K)(b)(a)600 K1000 K1100 K900 KAs-pressedRun 1Run 2Run 3Run 4Run 5 33 37334443414544The annealing pressures (GPa)are labeled near each plots43 8 2.3 Calculation of electronic structure  Based on the estimated amount of In, the electronic band structure of Th3P4-type In3S4, without In deficiency, at 40 GPa is depicted in Fig. 5 (a). Several electron bands cross the EF, indicating a metallic electronic state, which is consistent with our electrical transport measurements. The inset in Fig. 5 (b) presents the typical Hall resistance as a function of the applied magnetic field to determine the carrier type for the In3−xS4 obtained from transport measurements. The negative slope of the Hall resistance versus magnetic field indicates an n-type characteristic, which aligns with the results of band calculation. Figure 5 (b) shows the electronic DOS projected onto atomic orbitals. The bands crossing EF of In3S4 are mainly composed of In s, In p, and S p orbitals. Notably, the comparable contributions of In s and S p orbitals provide a high total-DOS at EF of 10 states/eV/unit cell at the conduction band bottom, which is twice that of Sn3S4[24]. The sharp peak in DOS near EF, resembling a van-Hove singularity (vHs), is advantageous for achieving high-Tc, similar to hydrides[39]. On the other hand, such singularity in the DOS possibly induces structural instability. The observed high Tc and rapid decomposition against a pressure change in In3−xS4 may be attributed to the vHs-like electronic states. Also, the complex DOS with sharp peaks is consistent with the dramatic changes in Tc observed in our experiments because the metal composition influences the carrier concentration, namely the position of EF. Additionally, a notable insight in the electronic states is the existence of an extremely high DOS, exceeding 23 states/eV/unit cell, located at the valence band top. This band is composed of only S p orbitals, similar to the electronic state of superconducting sulfur above 100 GPa. In a hole-doped In3−xS4, the realization of sulfur-dominant superconductivity at lower pressure is anticipated, such as in the case of high-Tc hydrides through the tuning of EF position via the defect-engineering and elemental substitution due to the unique feature of high degree of freedom in composing elements of Th3P4-type family.  FIG. 5. (a) Electronic band structure in In3S4 at 40 GPa. (b) Electronic density of states projected onto atomic orbitals in In3S4 at 40 GPa. The inset shows typical Hall resistance as a function of the applied magnetic field. (a)3210−1−2−3−4Energy (eV)Γ H N P HΓ04812162024-4 -3 -2 -1 0 1 2DOS (states/eV/unit cell)E-EF (eV)(b)TotalIn sIn pS sS p-4 -2 0 2 4-303μ0H (T)RH (mΩ) 9 2.4 Tc-P diagram in various sulfides Figure 6 displays the relationship between Tc and applied pressure (P) in various superconducting binary sulfides[51–59], Th3P4-type superconductors[24,51,60], and pure sulfur[61], as referring by a summary from previous paper[51]. In3S4 obviously exhibits a higher Tc than other isostructural Th3P4-type materials. It also holds the highest Tc record among all discovered sulfide superconductors, except for the high-Tc hydride H3S[62]. PbS has recently been reported to show a high Tc in sulfides at a moderate pressure of 19 GPa[51]. Electronic band calculations indicate that PbS has a similar electronic structure around EF as TaS2 and pure sulfur under high pressure, both of which show high Tc above 15 K and a significant contribution of the sulfur band to EF[51]. Therefore, the critical factor for achieving high Tc in sulfides is considered to be the sulfur band, which replicates the superconducting sulfur. Conversely, In3S4 exhibits a higher Tc than these sulfides at lower pressure regions despite comparable contributions of S and In bands to EF. Further investigation into the origin of the high Tc and the role of In is expected as further research topics. Recently, C. J. Pickard et al. proposed a figure of merit S-value for an evaluation of pressure-induced superconductivity as 𝑆=√𝑇c 𝑇c,MgB22 + 𝑃2⁄ , where the Tc of MgB2 is 39 K, and the S-value should be 1 in the case of MgB2 at ambient pressure[63]. Among binary sulfides, Th3P4-type In3S4 and Sn3S4 exhibit high S-value beyond 0.3, as shown in the dashed line of Fig. 6. This high S-value accelerates the exploration of practical superconducting materials within the metastable phases of the Th3P4-type cubic family.  FIG. 6. The Tc diagram against applied pressure in various superconducting binary sulfides, Th3P4-type superconductors, and pure sulfur[51–61], as referring by a summary from previous paper[51]. The dashed lines indicate a border for a figure of merit S for pressure-induced superconductivity.   51015201 10 100Critical temperature (K)La3-xS4La3-xSe4Sn3S4In3-xSe4PbSNbS2PdS2SnSPdS SnS2HfS3TaS2SMoS2Pressure (GPa)FeSIn3S4(This study) 10 3. Conclusion The highest Tc among the superconducting materials family has typically been discovered under high pressure. Due to their high degree of freedom in composing elements and tunable functionality, we have explored Th3P4-type cubic materials as a new vein for the superconducting family. This study demonstrates a series of experiments involving high-pressure synthesis, in-situ structural analysis, and electrical transport measurements of Th3P4-type In3−xS4 using a custom-designed DAC with BDD electrodes and heater. Key achievements of this study include i) the emergence of superconductivity in In3−xS4, ii) the anomalous enhancement of Tc up to 20 K, and iii) a unique electronic band structure. First, the starting material of tetragonal In2S3 undergoes several pressure-induced structural phase transitions and partially transforms into Th3P4-type In3−xS4 above 40 GPa without external heating. Although pressure-driven In3−xS4, namely In2.67S4, exhibits superconductivity at 9 K, its R-T curve remains semiconducting, and zero resistance is not observed. Thus, the transformation into superconducting Th3P4-type In3−xS4 is incomplete without annealing. Second, high-pressure annealing induces a clear metallic property, zero resistance in the superconducting state, and a single-phase SXRD pattern of Th3P4-type In3−xS4. The amount of In defect (x) in In3−xS4 systematically reduces with the increase of annealing temperature. A monotonic enhancement of Tc is observed with an optimal highest Tc of 20 K in In3S4 without In defects. This unexpectedly high Tc is the highest record among binary superconducting sulfides, excluding H3S. Finally, In3S4 exhibits a high DOS with comparable contributions from In and S orbitals at the conduction band bottom near EF, which differs from the electronic states of other high Tc sulfides. Additionally, a much higher DOS is located at the valence band top, composed of only the sulfur contribution.  Our findings on superconductivity in In3−xS4 open new avenues for both experimental and theoretical research fields to realize higher Tc in metastable materials because the Th3P4-type structure has high tunability in composing elements. Further exploration of related compounds in the Th3P4-type family is explored to understand the mechanism of anomalous superconductivity in In3−xS4.  Experimental section Preparation of DAC: For DAC experiments, the starting materials were placed into a sample chamber of DAC equipped with BDD electrodes[31–33] and heater[34] for high-pressure annealing, in-situ SXRD analysis, and electrical measurements. Single crystalline and nano-polycrystalline diamonds [64] were used for the anvil material. A Re sheet and cubic BN served as the sample chamber and pressure-transmitting medium. The applied pressure was estimated from the fluorescence of ruby powder[65] and peak shift in the Raman spectrum of the diamond anvil tip[66] using an inVia Raman Microscope (RENISHAW). R-T measurements were performed in a physical property measurement system (PPMS, Quantum Design) with a 7 T superconducting magnet.   11 High-pressure synthesis: Reproducible high-pressure synthesis was conducted through runs 1 to 5. High-pressure synthesis was performed in all runs using a custom-designed DAC with BDD components. In the run1, a mixture of orthorhombic InS and tetragonal In2S3 were used as starting materials with a stoichiometric composition of In:S=3:4. InS and In2S3 were synthesized via conventional melt and slow-cooling methods using In and S in an evacuated quartz tube. To obtain Th3P4-type In3−xS4, high-pressure annealing was performed at 33 (35) GPa and 960 K. In the run 2 to 5, only In2S3 was used for the synthesis. Conditions were 37 (38) GPa and 840 K in the run2, 33 (25) GPa and 840 K in the run3. In the runs 4 and 5, annealing was conducted several times for one sample. In the run4, the first sintering conditions were 44 (51) GPa and 680 K, and the second was 43 (43) GPa and 910 K. In the run5, the first sintering at 41 (43) GPa and 600 K, the second at 43 (45) GPa and 900 K, the third at 45 (44) GPa and 1000 K, and the fourth at 44 (45) GPa and 1100 K were performed. Pressure values naturally varied during the annealing cycles and those after sintering were indicated inside the parentheses. After all annealing treatments, the temperature dependence of resistance in the obtained samples was measured. The in-situ SXRD analysis was conducted after the annealing in the runs 3 and 5. Structural analysis: SXRD patterns and R-T curves were measured under corresponding pressures. SXRD measurements were carried out using synchrotron radiation at the AR-NE1A beamline in the Photon Factory (PF) located at the High Energy Accelerator Research Organization (KEK). The energy of X-ray beam was monochromatized to 30 keV (λ = 0.4171 Å). The X-ray is introduced to the sample in the DAC through a collimator with 50 μm diameter. SXRD patterns were integrated into a one-dimensional profile using IPAnalyzer, and lattice constants were determined using PDIndexer[67]. SXRD patterns were refined by Rietveld analysis using RIETAN-FP software[68] to estimate the occupancy in metal sites. Crystal structure images were generated using VESTA software[69].  Theoretical calculation: Electronic structures at high pressure was calculated using Quantum ESPRESSO (QE)[70–72]. The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE)[73] was used to describe the exchange-correlation function with the pseudopotentials obtained from the SSSP PBE Efficiency v1.3.0 library[74]. Stable atomic positions and lattice constants were calculated under pressure before the electronic structure calculations. A 8 × 8 × 8 k-grid was employed for the k-point sampling in the first Brillouin zone, and the kinetic energy cutoffs for the expansion of the electronic wave function were set to 50 Ry. A k-point mesh of 16 × 16 × 16 was used to calculate the DOS.   ACKNOWLEDGMENTS This work was partly supported by JSPS KAKENHI Grant Number 23H01835, 23K13549, and 23KK0088. The fabrication process of diamond electrodes was partially supported by the NIMS Nanofabrication Platform in the Nanotechnology Platform Project sponsored by the Ministry of  12 Education, Culture, Sports, Science and Technology (MEXT), Japan. The nano-polycrystalline diamond was synthesized and provided via the Visiting Researcher’s Program of the GRC with proposal No. 2023YB01. The synchrotron X-ray experiments were performed at AR-NE1A (KEK-PF) under the approval of proposal No. 2022G049 and 2024G084 with support from Dr. Y. Shibazaki (KEK). This work was supported by the World Premier International Research Center Initiative (WPI), MEXT, Japan.   References [1]  H. K. Onnes, Comm. Phys. Lab. Univ. Leiden-. 1911, 122, 124. [2]  S. Uchida, H. Takagi, K. Kitazawa, S. Tanaka, Jpn J Appl Phys 1987, 26, L1. [3]  J. G. Bednorz, K. A. Miiller, Condensed Possible High T c Superconductivity in the Ba-La-Cu-0 System, Vol. 64, 1986. [4]  Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J Am Chem Soc 2008, 130, 3296. [5]  L. Gao, Y. Y. Xue, F. Chen, Q. Xiong, R. L. Meng, D. Ramirez, C. W. Chu, J. H. Eggert, H. K. Mao, Phys Rev B 1994, 50, 4260(R). [6]  A. Yamamoto, N. Takeshita, C. Terakura, Y. Tokura, Nat Commun 2015, 6, 8990. 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Table of contents High-pressure synthesis and in-situ measurement of crystal structure and electrical transport properties using custom-design diamond anvil cell with boron-doped diamond electrodes reveals that Th3P4-type In3−xS4 exhibits an emergence of superconductivity with high Tc of 20 K under high pressure. The Tc is the highest record among all the superconducting sulfides except for hydrides.      00.010.020.0312 14 16 18 20 22Resistance (Ω)Temperature (K)In3−xS4 onBDD electrodes7 T0 T 16 Supplemental information for Emergence of Superconductivity at 20 K in Th3P4-type  In3−xS4 Synthesized by Diamond Anvil Cell with Boron-doped Diamond Electrodes   *R. Matsumoto1, K. Yamane1,2, T. Tadano3, K. Terashima1, T. Shinmei4, T. Irifune4, Y. Takano1,2 *Corresponding author; Email: MATSUMOTO.Ryo@nims.go.jp  1International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 2Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan 3Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan 4Geodynamics Research Center (GRC), Ehime University, Matsuyama, Ehime 790-8577, Japan    FIG. S1. Comparison of SXRD patterns between as-pressed In2S3 and sintered one under 41 GPa. The calculation patterns of Th3P4-type In3S4 cubic BN are also shown.  17   FIG. S2. SXRD patterns obtained In3−xS4 in the decompression process. The calculation patterns of Th3P4-type In3S4 cubic BN are also shown.   FIG. S3. (a) Temperature dependence of resistance in as-pressed In2S3 and obtained In3−xS4 under each pressure with log scale in resistance. (b) Enlarged plots around low temperature with liner scale in resistance.